机器学习-Random Sample Consensus Regression(RANSAC)回归

Section I: Brief Introduction on RANSAC

Linear regression models can be heavily impacted by the presence of outliers. In certain situations, a very small subset of our data can have a big effect on the estimated model coefficients. There are mant statistical tests that can be used to detect outliers. However, removing outliers always requiresour own judgement as data scientists as well as domain knowledge.

As an alternative to throwing out outliers, a robust method of regression using the random sample consensus (RANSAC) algorithm, which fits a regression model to a subset of the data, the so-called inliers. The iterative algorithm can be summarized as follows:

• Step 1: Select a random number of samples to be inliers and fit the model
• Step 2: Test all other data points against the fitted model and add those points that fall within a user-given tolerance to the inliers
• Step 3: Refit the model using all inliers
• Step 4: Estimate the error of the fitted model versus the inliers
• Step 5: Terminate the algorithm if the performance meets a certain user-defined threshold or if a fixed number of iterations were reached; go back to Step 1 otherwise.

FROM
Sebastian Raschka, Vahid Mirjalili. Python机器学习第二版. 南京：东南大学出版社，2018.

代码

from sklearn import datasets
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import PolynomialFeatures
from sklearn.metrics import mean_squared_error,r2_score
import matplotlib.pyplot as plt
import numpy as np
import warnings
warnings.filterwarnings("ignore")

plt.rcParams['figure.dpi']=200
plt.rcParams['savefig.dpi']